You resent the kids because they take up so much of your time and W's time, leaving you very little quality time with W. BUT, the reason this is so is because of how W handles her time, or mishandles it because of her (chosen) handicap. That is A LOT of stuff to be angry/resentful about.
Your W's refusal to get help is toxic to your M, and you are taking your anger and resentment out on your kids. Methinks.
BTW, I truly can't think of anything short of real abuse of some sort that is less attractive than being impatient/angry/raising voiceish with the kids. I'd say time to quit coddling the W and direct some of that anger/resentment towards the true source (her) rather than putting it on the kids.
Now, back to the part time job thing. If she can't go home during the day, she could certainly get a part time job to pay for a maid to do the cleaning that she is incapable of (currently and by choice) carrying out during the day.
Perhaps it could be a shared goal to have evenings free of almost all basic household chores. How can you work together to make this happen? The job/maid solution is a possible part of a solution. Perhaps you could also clean the kitchen well enough after dinner to last until morning.
Anyway, face the facts. I think this is what you really need to repeat to yourself.
1. W is incapacitated and debilitated by her panic disorder. 2. W is choosing to not get treatment for her panic disorder. 3. W's panic disorder significantly undermines our ability to have quality time together. 4. I react to W's panic disorder by living in a way that I resent. 5. I take out this resentment on my children. 6. I can do better with my children. 7. I acknowledge that I very much resent my W for not seeking treatment for her panic disorder. 8. I acknowledge that I am incredibly angry that W allows her panic disorder to severely undermine the possibility for a much better M than we have. 9. I want a better M than we have. 10. I cannot fix W, but I can quit enabling her behavior.